Further study is needed into the possuk “And I will write on the
luchos, the words that were on the first luchos that you broke”. This
seems to imply that exactly the same words were written and it seems
that we find differences between the first luchos in Parshas Yisro and
the second luchos in Parshas Voeschanan (and of course there are several differences).

What is the evidence that says that the second luchos are referred to in Parshas Voeschanan?

The Pesikta Rabasi here points out that the word "keep" is used in order to teach that Israel was instructed that only through "keeping" the Shabbos would they succeed in "keeping" the 2nd luchos from being lost like the 1st luchos. Here, likewise, the implication is that the account of the Aseres haDibros in Voeschanan records the text of the 2nd luchos, while the account in Yisro describes the text of the 1st luchos.

In clarifying the difference between the first and second luchos, the gemara in bava kama 55b highlights that the second luchos included the word "tov" while the first luchos did not. The word "yitav" a derivative of the word tov, is used in Parshas Va'eschanan when describing the reward of one who properly fulfills the commandment to honor one's parents, while in Parshas Yisro, this word is
omitted.